Absence of a Quadratic Term in the ⁴He Excitation Spectrum

Abstract

For many years it has been assumed that the long-wavelength portion of the ⁴He elementary excitation spectrum could be described by

$$\varepsilon \left( k \right)=c\hbar k\left( 1+{{\alpha }_{2}}{{k}^{2}}+... \right)\varepsilon \left( k \right)=c\hbar k\left( 1+{{\alpha }_{2}}{{k}^{2}}+... \right)$$

(1)

where e is the energy of the excitation, k is its wave number, and c is the sound velocity; α₂ is traditionally taken to be negative. Recently, however, Barucchi et al.¹ predicted that the excitation spectrum could be described by

$$\varepsilon \left( k \right)=c\hbar k\left( 1+{{\alpha }_{1}}k+{{\alpha }_{2}}{{k}^{2}}+... \right)$$

(2)

and Molinari and Regge² suggested that an improved fit to the inelastic neutron scattering data’ for the excitation spectrum could be achieved with this expression; α₁ was positive in the resultant fit.†

Based on work performed under the auspices of the U.S. Atomic Energy Commission.